Components of an Electric field due to a dipole

  • #1

Homework Statement


The problem is: Show that the components of [tex]\vec{E}[/tex] due to a dipole are given at distant points, by Ex=[tex]\frac{1}{4\pi\epsilon{o}}[/tex] [tex]\frac{3pxz}{(x^2+z^2)^{5/2}}[/tex] and Ez=[tex]\frac{1}{4\pi\epsilon{o}}[/tex] [tex]\frac{p(2z^2-x^2)}{(x^2+z^2)^(\frac{5}{2})}}[/tex]


http://physweb.bgu.ac.il/COURSES/PHYSICS2_B/2009A/homework/Homework-2_files/image006.jpg [Broken]

Homework Equations



E=[tex]\frac{1}{4\pi\epsilon{o}}[/tex] [tex]\frac{Q}{r^2}[/tex]
p=qd

The Attempt at a Solution



I have tried to break the fields of each one into vector components and add the components, however, it got really messy really quickly and after simplifying it a bit i got a ridiculous equation for just the x component, i had no clue where to go and gave up on even try to get the z component.

Ex=[tex]\frac{q}{4\pi\epsilon{o}}[/tex] [tex]\frac{(x^2+(z+\frac{d}{2})^{2})^{\frac{3}{2}}-(x^2+(z-\frac{d}{2})^{2})^{\frac{3}{2}}}{((x^{2}+z^{2})^{2} + (\frac{d^{2}x^{2}}{2}-\frac{d^{2}z^{2}}{2}+\frac{d^4}{16}))^{\frac{3}{2}}}[/tex]
 
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